Spectral density of bitcoin transaction rates

Suggested reading:
http://organofcorti.blogspot.com/2014/11/daily-and-weekly-bitcoin-transaction.html
http://en.wikipedia.org/wiki/Spectral_density

0. Introduction
A few readers pointed out to me that spectral density analysis of transaction volume should show peaks at the frequencies I assumed to exist - i.e. one 'per week' cycle and one 'per day' cycle, which would further validate the decomposition from the previous post, and also allow me to show off a little.

Data for this post is here. Unfortunately only post-2012 data fits, in the bin, but it should be sufficient if you want to try your own approach.


1. Spectral density
In this type of time series analysis the frequency domain is analysed, rather than the time domain. We expect spikes in the output that correspond to frequencies at which define the cycles in the data. This was my first effort:

Converting the power to dB, cycles per hour to cycles per week and smoothing the spectrum somewhat, we have:

The weekly and daily cycles are the first and third peaks.  I checked the spectral F stats which also picked these four peaks as the significant ones.

I'm not sure the second and fourth peaks - biweekly and twelve hourly - make a great deal of sense. Interestingly, they're both one octave above both weekly and daily rates, the second harmonics if you consider the first and third peaks to be the fundamentals. Spectral analysis isn't something I've done since university, so if someone knows why this might be the case, let me know.

Edit: See the comments below for an explanation of the second harmonics.

2. Spectral density animation, with accompaniment.
The daily cycle seems to have appeared early on, in 2011. The others appeared in 2013 onward. It's interesting that although the weekly cycle is clearly there in 2013, that wasn't at all obvious from viewing the daily transactions plots.

Important note: The youtube link below is the correct soundtrack for viewing this gif - or at least it was the one I had when making it. Seems to be just right.

3. Summary

• Intra-day transaction rate cycles have existed since 2011
• Intra-week transaction cycles began to appear in 2013.
• Neither of these were clearly evident when viewing this data in the time domain until late 2013 / early 2014.
• Crystal Castles improves ones appreciation of spectral analysis of bitcoin transaction rates.

Thanks to readers Bob and Daniele for pointing out that I really should have done this in the first place.






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